is there a nat device on the network? A lot of nat devices will support the first vpn user (the ports used for VPN are mapped for the first host). Subsequent users cannot get a connection because the ports are already in use.
First check out what the perimiter network device is and wheather you can make any changes to it.
The second thing to investigate is the client software, you have the option to fiddle with options for dealing with NAT by playing with the TCP and UDP ports used. Now I know that these are supported by the VPN concentrators, I'm not sure if the PIX currently supports these options. Maybe in v7.0